Analysis of higher order time delay systems using Lambert W function

Use of the Lambert W function for time-domain analysis of feedback fractional delay systems

The Lambert W function is defined as the multivalued inverse of the function w ! we 1⁄4 z. It has been applied to stability analysis of a class of fractional delay systems whose transcendental characteristic equation (TCE) can be remodelled in the form (asþ b)eþ d 1⁄4 0. The approach of using the Lambert W function to time-domain analysis of a class of feedback fractional-order time-delay syste...

Time-Delay Estimation using the Characteristic Roots of Delay Differential Equations

Problem statement: For ordinary dynamic systems (i.e., non-delayed), various methods such as linear least-squares, gradient-weighted least-squares, Kalman filtering and other robust techniques have been widely used in signal processing, robotics, civil engineering. On the other hand, time-delay estimation of systems with unknown time-delay is still a challenging problem due to difficulty in for...

Survey on Analysis of Time Delayed Systems via the Lambert W Function

This paper summarizes recent research on an approach for the analytical solution to systems of delay differential equations developed using the Lambert W function [26, 29], and its applications [25, 28]. Also, several outstanding research problems associated with the solution of systems of delay differential equations using the matrix Lambert W function are highlighted. The solution has the for...

Delay differential equations via the matrix Lambert W function and bifurcation analysis: application to machine tool chatter.

In a turning process modeled using delay differential equations (DDEs), we investigate the stability of the regenerative machine tool chatter problem. An approach using the matrix Lambert W function for the analytical solution to systems of delay differential equations is applied to this problem and compared with the result obtained using a bifurcation analysis. The Lambert W function, known to...

Time-delay Systems: Analysis and Control Using the Lambert W Function